Study on the Dynamic Behavior of a Class of Heterogeneous Network Systems With Time Delay

Abstract

Successful treatment of COVID-19 that outbroke worldwide since the beginning of 2020 has demonstrated the importance of effective isolation, which is aimed at asymptomatic and symptomatic infected persons in the incubation period. In this paper, to further analyze the transmission dynamics behavior of epidemics with the latent state, we construct a class of health state - latent state - infection - recovery state (SEIR) infectious disease model with heterogeneity and time delay characteristic based on considering the nonlinear incidence rate formed by psychological inhibition factors. Also, the dynamics of the epidemic, the threshold condition, and stability are studied by creating Lyapunov functions reasonably, applying LaSalle's Invariance Principle and mean-field equation theory. The research shows that, the basic reproduction number R0 of the system depends on birth rate, death rate, recovery rate, disease transmission rate, and network topology. If R0 <; 1, the system is stable at the disease-free equilibrium point E0, and if R0 > 1, the system is sound at the endemic equilibrium point E*. Moreover, it is also proved that latent delay and psychological inhibitory factors can influence the peak and rate of the infected nodes in the system before their convergence to the equilibrium point, but not the system's global stability. Meanwhile, the theoretical results are verified by numerical simulation finally.

Keywords

• Asymptotic stability
• heterogeneity
• Lyapunov functions
• psychological inhibition
• time delay